Theorem orim2d 800

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 798	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

This proof depends on syntax axioms:   -> wi 4   \/ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  orim2  801  orbi2d  802  pm2.82  824  stdcndcOLD  858  pm2.13dc  897  exmid1dc  4339  acexmidlemcase  6083  poxp  6472  fodjuomnilemdc  7490  omniwomnimkv  7513  exmidontriimlem1  7583  indpi  7715  suplocexprlemloc  8094  nneoor  9759  uzp1  9972  maxabslemlub  11996  xrmaxiflemlub  12039  nninfctlemfo  12842  exmidunben  13375  bj-nn0suc  17195  sbthomlem  17276